# ParetoFlow: Guided Flows in Multi-Objective Optimization

arXiv: https://arxiv.org/abs/2412.03718 · HTML: https://mlsanity.com/paper/2412.03718/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 67 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 30 of 43)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search](https://mlsanity.com/paper/2001.00326/) (2020)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [HW-NAS-Bench:Hardware-Aware Neural Architecture Search Benchmark](https://mlsanity.com/paper/2103.10584/) (2021)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (2021)
- [Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation](https://mlsanity.com/paper/2102.07970/) (2021)
- [Bidirectional Learning for Offline Infinite-width Model-based Optimization](https://mlsanity.com/paper/2209.07507/) (2022)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Structure-aware Protein Self-supervised Learning](https://mlsanity.com/paper/2204.04213/) (2022)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [Importance-aware Co-teaching for Offline Model-based Optimization](https://mlsanity.com/paper/2309.11600/) (2023)

## Built on by (most cited first, 17 of 17)

- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Design](https://mlsanity.com/paper/2505.07086/) (2025)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Preference-Guided Diffusion for Multi-Objective Offline Optimization](https://mlsanity.com/paper/2503.17299/) (2025)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)
- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimization](https://mlsanity.com/paper/2509.03244/) (2025)
- [SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion](https://mlsanity.com/paper/2509.21058/) (2025)
- [Pareto-Conditioned Diffusion Models for Offline Multi-Objective Optimization](https://mlsanity.com/paper/2602.00737/) (2026)
- [AffinityFlow: Guided Flows for Antibody Affinity Maturation](https://mlsanity.com/paper/2502.10365/) (2025)
- [Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimization](https://mlsanity.com/paper/2506.05680/) (2025)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)
- [Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization](https://mlsanity.com/paper/2605.11246/) (2026)
- [Sample-Efficient Optimisation over the Outputs of Generative Models](https://mlsanity.com/paper/2509.23800/) (2025)
- [The Offline-Frontier Shift: Diagnosing Distributional Limits in Generative Multi-Objective Optimization](https://mlsanity.com/paper/2602.11126/) (2026)
- [Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization](https://mlsanity.com/paper/2605.12106/) (2026)
- [ParetoTransport: Generative Optimization by Mass Transport Toward The Pareto Front](https://mlsanity.com/paper/2609.07706/) (2026)

## Abstract (arXiv)

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.